Two scenes that always bothered me are both in "Journey To Babel"
First, before his final confrontation with Sarek, Gav is sitting against the wall having a drink, and the drink switches hands (count 'em) FOUR times!!! Once in a while you can get away with bad editing, but this is SO OBVIOUS.
Later, when Kirk is fighting the Orion spy, he does this bizarre drop kick-thing. He seem to aim for the wall, nowhere near the fake Andorian. I don't know what the heck he was going for, but it just looks so stupid, I laugh every time.